A p-adic analogue of a formula of Ramanujan

Dermot McCarthy, Robert Osburn

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures.

Original languageEnglish
Pages (from-to)492-504
Number of pages13
JournalArchiv der Mathematik
Volume91
Issue number6
DOIs
StatePublished - Dec 2008

Keywords

  • Gaussian hypergeometric series
  • Supercongruences

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